(cf. [1]}).
If \((\pi , \mathcal {H})\)  is smooth, then the
invariance of \(\mathcal {H}^\infty \)  under \(\pi (G)\)  implies that
the operators \(i {\tt d}\pi (x)\) , \(x \in {\mathfrak {g}}\) , on this space
are essentially selfadjoint (cf. [2]},
[3]}).

